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We appreciate your visit to In triangle MNO and triangle PQR angle MNO cong angle PQR and overline NO cong overline QR What additional congruence is needed to prove that. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!

In \( \triangle MNO \) and \( \triangle PQR \), \(\angle MNO \cong \angle PQR\) and \( \overline{NO} \cong \overline{QR} \).

What additional congruence is needed to prove that \( \triangle MNO \) and \( \triangle PQR \) are congruent by the SAS postulate?

A. \(\overline{MN} \cong \overline{PQ}\)

B. \(\overline{MO} \cong \overline{PR}\)

C. \(\overline{MN} \cong \overline{QR}\)

D. \(\overline{MO} \cong \overline{PQ}\)

Answer :

Final answer:

To prove congruent triangle using the SAS postulate, the additional congruence of Side MO ≅ Side PR is needed.

d) Side MO ≅ Side PQ

Explanation:

To prove that Δmno and Δpqr are congruent by the SAS (Side-Angle-Side) postulate, we need the additional congruence of Side MO ≅ Side PR.

Let's break it down step-by-step:

  1. Given: ∠mno ≅ ∠pqr and NO ≅ QR
  2. To prove: Δmno and Δpqr are congruent by SAS postulate
  3. Additional congruence needed: Side MO ≅ Side PR
  4. Reason for additional congruence: SAS postulate requires two pairs of corresponding sides and one pair of corresponding angles to be congruent.

Therefore, the correct answer is: d) Side MO ≅ Side PQ.

Learn more about Congruent Triangles here:

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